The marble slabs covering the walls of the S. Maria dei Miracoli church in Venice are suffering serious degradation due to the combined physical and chemical action of soluble salts. The church walls have a high moisture content due to rain penetration. Laboratory tests and field measurements of the moisture content in various areas of the walls are currently in progress to investigaye the thermal and hygrometric characteristics of the marble slabs covering. The data concerning the indoor climate and its influence on the phenomena are also considered. Knowing the boundary conditions (indoor climate) and using the preliminary data available for the constituting materials (marble), a tentative analysis of the moisture migration in the marble slabs is performed using a numerical model of the heat and mass transfer in porous media. It is shown that the moisture migration, and hance the damages, could be reduced by having a ventilated space between the slabs. -- CAL